Ashley P.

asked • 05/23/22

Locus of a Sphere

A sphere of constant radius k passes through the origin O and meets the axes in A, B, C. Prove that the locus of the centroid of triangle ABC is the sphere 9(x^2 + y^2 + z^2) = 4(k^2)

Dayv O.

how does sphere pass through origin with locus equation provided? if x,y,z=0 equation has no solution.Plugging in (0,0,0) should result in r=r. If there is circle, passing through origin, centered at (1,0) equation would be (x-1)^2+y^2=1.At (0,0) 1=1.
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05/23/22

Dayv O.

The way the equation is written, the center of the sphere is origin. So the axis intercepts would be equal to radius.
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05/23/22

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